Existence of Sauron in The Hobbit

A lot of this is original dialog written for The Hobbit movie intended to link it with The Lord of the Rings, and to give them enough story to expand the short novel to three movies. The novel has no such scene in it, however information about The Necromancer who inhabits Dol Guldur can be found in TLOTR.

At the time of The Hobbit, it is presumed that Sauron's defeat when the ring is cut from his hand and lost 'forever' was final. We know from TLOTR that this is not true, and by the time that Bilbo relinquishes the ring and we are first made aware of him in the story, Sauron has re-inhabited Barad Dur in Mordor and is rebuilding his army openly. The movies of the Hobbit are going to try to bridge that gap.

It is revealed in the backstory of the novel of TLOTR that the Necromancer of Dol Guldur is Sauron, who has chosen that location because it is close to the Gladden Fields where he believes the ring was lost. Relatively weak he has not revealed who he is, but his influence has changed Greenwood the Great, and is has become a more dangerous place renamed Mirkwood. Gandalf sets out and discovers that the Necromancer is Sauron, and carries that information back to the White Council.

You have not missed anything yet in the story. I suspect we will see all of the above story, and what the White Council chooses to do with that information in Parts II and III of the movies.

The Necromancer is indeed Sauron himself, but from what I gather, he was never mentioned by name in The Hobbit.

In chapter seven of the book — “Queer Lodgings” — Gandalf is about to leave the party, and explains the route the rest must take. When Bilbo inquires if there was some safer indirect way, Gandalf says “There are no safe paths in this part of the world”, and proceeds to enumerate the dangers, one of which being the Necromancer:

Before you could get round it [Mirkwood] in the South, you would get into the land of the Necromancer; and even you, Bilbo, won’t need me to tell you tales of that black sorcerer. I don’t advise you to go anywhere near the places overlooked by his dark tower!

In The Hobbit edition annotated by Douglas A. Andersen there is a respective note on page 188:

The reintroduction of the Necromancer here was originally quite casual; his function, as Tolkien wrote in a letter to Christopher Bretherton on July 16, 1964, was “hardly more than to provide a reason for Gandalf going away and leaving Bilbo and the Dwarves to fend for themselves, which was necessary for the tale”.

And on page 57 (chapter one), in the note about Thorin’s father being imprisoned by the Necromancer:

In The Lord of the Rings, we learn that the Necromancer of The Hobbit is also the Dark Lord, or Sauron…

Thus, in the book, the Necromancer is mentioned grand total of two times, and the name Sauron never appears. I suppose, for the film adaptation they deliberately made it more obvious to better connect with the subsequent trilogy for those who are not well versed in the LotR universe, including myself. Ironically, I had missed that connection in the film (going to have to pay attention when I re-watch it), and only caught on to this, because of the marvelous book I have.